Classification of pairing phase transition in metal clusters in vanadium and aluminum particles using Grossman theory

In this work, the phase transition from normal to superconductivity state of two metal clusters, vanadium and aluminum particles, are theoretically studied by changing size and resistance parameter. We obtained the heat capacity integral of Grossman's theory considering that the first zero of the partition functions is located in the complex temperature plane. Then, we used the experimental data of the heat capacity of aluminum metal clusters and vanadium particles to determine the unknown integral coefficients of the heat capacity of Grossman's theory. Based on the obtained coefficients, we discussed the classification of the phase transition of the aforementioned metal clusters. Also, the obtained coefficients have been used to plot the heat capacity of aluminum metal clusters and vanadium particles. Finally, we compared the obtained heat capacity with the experimental results. A good agreement between our results and the experimental data has been obtained.